Question

How can one fifth x − 2 = one third x + 8 be set up as a system of equations?

A. 5y − 5x = −10
3y − 3x = 24

B. 5y − 5x = −10
3y + 3x = 24

C. 5y + x = −10
3y + x = 24

D. 5y − x = −10
3y − x = 24

Answer 1

none of the above

Explanation:

The given equation can be divided into two parts:

... x - 2 = y = (1/3)x +8

Putting the left equation into standard form, it becomes

... y -x = -2

Multiplying it by 5 gives ...

... 5y -5x = -10 . . . . . . . . . . . matches answer choices A or B

Please note there is no obvious reason why the equation is multiplied by 5. (It is no longer in standard form when there is a factor of 5 that can be removed.)

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Putting the right equation into standard form, it becomes

... y = (1/3)x + 8

... 3y = x + 24 . . . . . multiply by 3

... 3y -x = 24 . . . . . . subtract x . . . . . . matches answer choice D

Solution:

An appropriate system of equations is ...

• 5y -5x = -10
• 3y -x = 24

These have solution (x, y) = (15, 13) as the original equation does.

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Comment on the question

In cases like this, where none of the offered answers has any relevance to the problem, I suggest you have your teacher show you how to work this problem and check the resulting answer.